Rotating each iteration of an Array Modifier
You can achieve that with the Array modifier alone.


Create an empty at the origin of your base pair and make sure it has the same xyz rotation.
Disable all offsets in the Array modifier.
Enable Object Offset and select the empty from the list.
Rotate the empty and move it up a little, so that it matches your helix. 


The object offset uses the differences regarding location, rotation and scale to generate the array.



Another, older and in some aspects, more powerful way would be to animate the base pair rotating and moving up the helix and then turn on dupliframes in the Duplication panel of the object properties.

To get even spaces between the steps, you'd have to set the f-curve to linear interpolation.